Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Rachel98

  • 3 years ago

I don't really get this. Question: Use the rules for exponents and roots to prove that 512^2/3 = 16^3/2

  • This Question is Closed
  1. mjr632
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Do you mean a rigorous formal proof?

  2. Rachel98
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I don't really know. This is what the question was and I don't get it.

  3. mjr632
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Do you understand how to use logarithms?

  4. Rachel98
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    No

  5. mjr632
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Ah, you will want to understand natural logarithms for this question, I can explain it.

  6. mjr632
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[y = \log_b x\] \[x = b^y\]

  7. mjr632
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    If we take the natural logarithm of \[512^{\frac{2}{3}}\] \[\frac{2}{3}\ln(512)\]

  8. mjr632
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    We can pull the exponent out

  9. Rachel98
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So, is that a cube root? That we ended up with?

  10. precal
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1360950294527:dw|

  11. precal
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1360950347726:dw|

  12. precal
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1360950360574:dw|

  13. precal
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1360950390774:dw|

  14. precal
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1360950432326:dw|

  15. precal
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes they are both equivalent

  16. Rachel98
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Thanks, so much. That makes sense now.

  17. precal
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yw

  18. precal
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    no need to use logs here

  19. ghass1978
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    just using exponents :512=2^9 so 512^(2/3)=2^6 and 16^(3/2)=2^6 so both are equal

  20. Rachel98
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Thanks

  21. precal
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yw

  22. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy